ACTIVITY 2.5
COMMUTATIVITY OF THE THREE OR MORE VECTORS ADDITION

In this activity we will prove the commutativity of the vector sum working with components.

If= (a ₁, a ₂) and= (b ₁, b ₂), then

+= (a ₁, a ₂) + (b ₁, b ₂) = (a ₁ +b ₁ , a ₂ +b ₂)
              = (b ₁ + a ₁, b ₂ + a ₂) =+

You observe that the demonstration that we have made is based on the commutativity of the numbers sum.

Also it is easy to see if we work with components that the commutativity of the sum can apply to any more than two vectors sum:
++ =++ =++ =++ =++= ... etc.

INTERACTIVE ACTIVITY

You have a construction that represents the sum of vectors =++. You can move the three vectors, and Moving the corresponding green point.

1) You make a construction that represents it     sum of =++. That is to say, you change the order of the adding and you check that you obtain the same vector.
2) You repeat the construction representing now the sum =++.
3) Finally, you represent as the sum of three vectors, and In an order different of the two previous.

He observe that when we work with components it also verifies the commutativity of the three vectors sum.

SOLUTION

1)  ++

END OF ACTIVITY 2.5
COMMUTATIVITY OF THE THREE OR MORE VECTORS ADDITION